An alternating binary number triangle grows one digit per row, printing 0 or 1 from j % 2 as the inner index counts down.
Rule: outer i = 1..rows; inner j = i..1; print j % 2
1
01
101
0101
10101 ← rows = 5In Python you solve it with an ascending outer loop and a descending inner loop: print(j % 2, end="") prints each bit, then bare print() ends the row. Program 16 flips the inner direction (1..i) for a related shape.
Outer loop from 1 to rows. Inner loop from current i down to 1, printing j % 2. End each row with print().
| Method | Idea | Best for |
|---|---|---|
Descending + j % 2 | Count j down; print parity as the bit | Learning, interviews, exams |
| Flip bits | Print 1 - (j % 2) | Complementary triangle labs |
for i from 1 to rows:
for j from i down to 1:
print j % 2 (no newline)
print newline| Goal | Pattern |
|---|---|
| Grow row length | for i in range(1, rows + 1): |
| Print binary digit | for j in range(i, 0, -1): print(j % 2, end="") |
| End the row | print() |
| Flip every bit | print(1 - (j % 2), end="") |
| Program 16 twin | for j in range(1, i + 1): print(j % 2, end="") |
| API | Effect | Use for |
|---|---|---|
print(j % 2, end="") | Stays on the same line | Each binary digit |
print() | Ends the current line | After the inner loop |
Print all bits without a newline, then end the row once.
Change the row count and the binary triangle updates instantly.
Trace three outer values when rows = 5 — watch j % 2 flip as j counts down.
i | Inner j | j % 2 | Printed row |
|---|---|---|---|
1 | 1 | 1 | 1 |
2 | 2, 1 | 0, 1 | 01 |
3 | 3, 2, 1 | 1, 0, 1 | 101 |
5 | 5..1 | 1,0,1,0,1 | 10101 |
Total digits are 1+2+3+4+5 = 15 — the triangular number n(n+1)/2.
Three complete programs: fixed height, flipped bits, and input(). Use View Output for sample results.
rows = 5Outer grows, inner counts down, print j % 2.
rows = 5
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j % 2, end="")
print()1. Outer grows the length. i runs from 1 to rows — that is how many bits each row gets.
2. Inner prints parity. j counts down from i to 1; j % 2 is the bit.
3. End the row. Call bare print() only after the inner loop finishes.
1 - (j % 2)Invert every bit so the first row starts with 0 instead of 1.
rows = 5
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(1 - (j % 2), end="")
print()1. Same loop bounds. Outer and inner ranges match Example 1.
2. Flip the bit. 1 - (j % 2) turns 1 into 0 and 0 into 1.
3. First row becomes 0. Useful when a lab asks for the complementary binary triangle.
Read the row count from the keyboard. Prefer a try / except in real apps (shown in the tip below).
rows = int(input("Enter the number of rows: "))
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j % 2, end="")
print()1. Same loop core. Only the source of rows changes from a literal to keyboard input.
2. Entering 4 stops early. You get four binary rows ending at 0101.
3. Safer input tip. Bare int(input()) raises ValueError on letters. Prefer:
raw = input("Enter the number of rows: ").strip()
try:
rows = int(raw)
except ValueError:
print("Enter a positive whole number.")
raise SystemExit(1)
if rows < 1:
print("Enter a positive whole number.")
raise SystemExit(1)Check these before calling the solution done.
for j in range(1, i + 1)That is Program 16 (1, 10, 101). Keep counting down for this pattern.
print(j, end="") instead of print(j % 2, end="")That prints the countdown numbers. This pattern needs the parity bit only.
print(j % 2) inside the inner loopThat puts each bit on its own line. Use print(j % 2, end="") for bits; call bare print() only after the row finishes.
Output is just 1 — a good sanity check.
The outer loop never runs. Validate and prompt again for clearer UX.
The classic sample is concatenated (10101), not spaced (1 0 1 0 1).
| Program | Time | Extra space |
|---|---|---|
| Fixed / flip / input (Examples 1–3) | O(n²) | O(1) |
There are n rows printing 1+2+…+n bits, so total work is n(n+1)/2.
i, print j % 2 while j counts from i down to 1.j → 0; odd j → 1.print() advances after each row.1, 10, 101…One line: for each row length i, print j % 2 from i down to 1 with end="", then call print().
Each row prints alternating 0 and 1 using j % 2. The inner loop counts down with range(i, 0, -1), so row length grows each line — still O(n²) total prints.
Continue with the ascending-inner twin that starts each row with 1.
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